Explicit computations of Serre’s obstruction for genus-3 curves and application to optimal curves

DOI10.1112/S1461157009000576zbMath1278.11068arXiv0901.2920OpenAlexW1970574333MaRDI QIDQ3091997

Christophe Ritzenthaler

Publication date: 15 September 2011

Published in: LMS Journal of Computation and Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0901.2920

Mathematics Subject Classification ID

Curves over finite and local fields (11G20) Arithmetic ground fields for abelian varieties (14K15) Varieties over finite and local fields (11G25)

Related Items (7)

Courbes de genre \boldmath3 avec \boldmath𝑆₃ comme groupe d’automorphismes ⋮ Large Galois images for Jacobian varieties of genus 3 curves ⋮ Principally polarized squares of elliptic curves with field of moduli equal to \(\mathbb{Q}\) ⋮ Distributions of Traces of Frobenius for Smooth Plane Curves Over Finite Fields ⋮ Optimal curves over finite fields with discriminant \(-19\) ⋮ Spanning the isogeny class of a power of an elliptic curve ⋮ Parametrizing the moduli space of curves and applications to smooth plane quartics over finite fields

Cites Work

• Unnamed Item
• Jacobians in isogeny classes of abelian surfaces over finite fields
• Arithmetic on elliptic curves with complex multiplication. With an appendix by B. Mazur
• On some questions of Serre on abelian threefolds
• Abelian varieties over finite fields

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